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An adaptive mutation for cartesian genetic programming using an \(\epsilon \)-greedy strategy

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Abstract

The optimization of the number of transistors of combinational logic circuits can lead to faster and cheaper electronic devices, but it is an NP-complete problem. There are deterministic algorithms for this task, but their effectiveness is limited to small problems. Thus, the use of metaheuristics is suitable and Cartesian Genetic Programming (CGP) is widely adopted in the literature. In CGP, mutation is commonly the only operator used for generating new candidate solutions. As a result, the performance of this metaheuristic is dependent on the proper choice of mutation and its parameters. CGP mutation is usually based on uniform mutation and, thus, any modification has the same chance to occur. In order to improve the performance of CGP, a study of the mutation operator is carried out and an adaptive approach using an \(\epsilon \)-greedy strategy for bias the selection of the node mutation type is proposed here. The proposal is evaluated using a benchmark from the literature. The results obtained indicate that the proposed adaptive mutation is promising, achieving the best mean results in 19 out of the 23 benchmark problems considered here. We also verified a better ability in generating feasible solutions than the standard CGP.

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Data Availability

The algorithm proposed in this research, as well as the data produced by it, can be found in the following repository: https://github.com/FMoller/cgp-rl. The main Author is also willing to send the research data, in case of any problem with the repository, via e-mail: fredericomollerped@gmail.com.

Notes

  1. A comparison between the static and adaptive bias methods can be seen at https://github.com/FMoller/cgp-rl in the Comparison of CGP-RL and SAM+2G+P folder

  2. Some experiments were carried out in order to analyze how mutations in each node element influence the generation of better CLCs. These experiments were performed using CGP with SAM and not with the proposed method and can be accessed at: https://github.com/FMoller/cgp-rl, in the Analysis of CGP’s evolutionary process folder.

  3. The source code of the proposed Node CGP-RL is available at https://github.com/FMoller/cgp-rl.

  4. The experiments presented in this article are related to the main objective of the proposed method: to improve the ability of the CGP to minimize the number of transistors in CLCs. A complementary analysis was carried out, with the objective of analyzing the convergence toward a feasible solution. This analysis is available at https://github.com/FMoller/cgp-rl, in the Node CGP-RL folder Convergence towards a feasible solution.

  5. It is not possible to determine statistical significance for the cmb problem, as the reference algorithm, CGP with SAM mutation, did not generate feasible results.

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Authors and Affiliations

  1. Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil

    Frederico José Dias Möller, Heder Soares Bernardino, Stênio Sã Rosário Furtado Soares & Lucas Augusto Müller de Souza

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  1. Frederico José Dias Möller
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  2. Heder Soares Bernardino
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  3. Stênio Sã Rosário Furtado Soares
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  4. Lucas Augusto Müller de Souza
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Frederico Möller, Heder Soares Bernardino, Stênio Sã Rosário Furtado Soares and Lucas Augusto Müller de Souza. The first draft of the manuscript was written by Frederico Möller and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Frederico José Dias Möller.

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Ethical and informed consent for data used

The authors declare that they have no conflict of interest regarding the research carried out and the data produced. The research does not involve testing on humans or animals. The authors are aware of and consent to the publication of data resulting from this research.

Competing Interests

This study was funded by Conselho Nacional de Desenvolvimento Científico e Tecnológico, under Grant Agreement No (316801/2021-6), by Fundação de Amparo á Pesquisa do Estado de Minas Gerais, under Grant Agreement No (APQ-00337-18), and bu Federal University of Juiz de Fora.

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This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. Also, the authors thank the support of CNPq (316801/2021-6), FAPEMIG (APQ-00337-18), and UFJF. Also, this work has been supported by UFJF’s High-Speed Integrated Research Network (RePesq).We also thank Professor Helio Barbosa, for pointing out the issue of Not gate bias.

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Möller, F.J.D., Bernardino, H.S., Soares, S.S.R.F. et al. An adaptive mutation for cartesian genetic programming using an \(\epsilon \)-greedy strategy. Appl Intell 53, 27290–27303 (2023). https://doi.org/10.1007/s10489-023-04951-4

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